U Zʹj)@sdZddlmZddlmZddlmZmZddlm Z m Z ddl m Z m Z ddlmZmZmZmZmZddlmZdd lmZdd lmZdd lmZGd d d e ZdS)z4Parabolic geometrical entity. Contains * Parabola )S)ordered)_symbolsymbols)GeometryEntity GeometrySet)PointPoint2D)LineLine2DRay2D Segment2DLinearEntity3D)Ellipse)sign)simplify)solvec@seZdZdZdddZeddZeddZed d Zed d Z dddZ eddZ eddZ ddZ eddZeddZdS)ParabolaaA parabolic GeometryEntity. A parabola is declared with a point, that is called 'focus', and a line, that is called 'directrix'. Only vertical or horizontal parabolas are currently supported. Parameters ========== focus : Point Default value is Point(0, 0) directrix : Line Attributes ========== focus directrix axis of symmetry focal length p parameter vertex eccentricity Raises ====== ValueError When `focus` is not a two dimensional point. When `focus` is a point of directrix. NotImplementedError When `directrix` is neither horizontal nor vertical. Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7,8))) >>> p1.focus Point2D(0, 0) >>> p1.directrix Line2D(Point2D(5, 8), Point2D(7, 8)) NcKsH|rt|dd}n tdd}t|}||r6tdtj|||f|S)N)dimrz*The focus must not be a point of directrix)rr contains ValueErrorr__new__)clsfocus directrixkwargsrV/var/www/html/bwave/python/venv/lib/python3.8/site-packages/sympy/geometry/parabola.pyrAs  zParabola.__new__cCsdS)aXReturns the ambient dimension of parabola. Returns ======= ambient_dimension : integer Examples ======== >>> from sympy import Parabola, Point, Line >>> f1 = Point(0, 0) >>> p1 = Parabola(f1, Line(Point(5, 8), Point(7, 8))) >>> p1.ambient_dimension 2 rrselfrrrambient_dimensionOszParabola.ambient_dimensioncCs|j|jS)aReturn the axis of symmetry of the parabola: a line perpendicular to the directrix passing through the focus. Returns ======= axis_of_symmetry : Line See Also ======== sympy.geometry.line.Line Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.axis_of_symmetry Line2D(Point2D(0, 0), Point2D(0, 1)) )rZperpendicular_linerrrrraxis_of_symmetrydszParabola.axis_of_symmetrycCs |jdS)aThe directrix of the parabola. Returns ======= directrix : Line See Also ======== sympy.geometry.line.Line Examples ======== >>> from sympy import Parabola, Point, Line >>> l1 = Line(Point(5, 8), Point(7, 8)) >>> p1 = Parabola(Point(0, 0), l1) >>> p1.directrix Line2D(Point2D(5, 8), Point2D(7, 8)) argsrrrrr~szParabola.directrixcCstjS)aThe eccentricity of the parabola. Returns ======= eccentricity : number A parabola may also be characterized as a conic section with an eccentricity of 1. As a consequence of this, all parabolas are similar, meaning that while they can be different sizes, they are all the same shape. See Also ======== https://en.wikipedia.org/wiki/Parabola Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.eccentricity 1 Notes ----- The eccentricity for every Parabola is 1 by definition. )rZOnerrrr eccentricitys!zParabola.eccentricityxyc Cst|dd}t|dd}|jj}|tjkrRd|j||jj}||jjd}n|dkrd|j||jj}||jjd}nX|j \}}|jj dd\}} ||d||d}|j ||d|d| d}||S)azThe equation of the parabola. Parameters ========== x : str, optional Label for the x-axis. Default value is 'x'. y : str, optional Label for the y-axis. Default value is 'y'. Returns ======= equation : SymPy expression Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.equation() -x**2 - 16*y + 64 >>> p1.equation('f') -f**2 - 16*y + 64 >>> p1.equation(y='z') -x**2 - 16*z + 64 TrealrrN) rrsloperInfinity p_parametervertexr'r(r coefficientsequation) r r'r(mt1t2abcdrrrr1s    "zParabola.equationcCs|j|j}|d}|S)aYThe focal length of the parabola. Returns ======= focal_lenght : number or symbolic expression Notes ===== The distance between the vertex and the focus (or the vertex and directrix), measured along the axis of symmetry, is the "focal length". See Also ======== https://en.wikipedia.org/wiki/Parabola Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.focal_length 4 r)rdistancer)r r9 focal_lengthrrrr:szParabola.focal_lengthcCs |jdS)aThe focus of the parabola. Returns ======= focus : Point See Also ======== sympy.geometry.point.Point Examples ======== >>> from sympy import Parabola, Point, Line >>> f1 = Point(0, 0) >>> p1 = Parabola(f1, Line(Point(5, 8), Point(7, 8))) >>> p1.focus Point2D(0, 0) rr$rrrrr szParabola.focuscs^tddd\}}|}ttrb|kr0gSttddt|g||gdddDSnttrt| |j df|j dfgdkrgSgSntt t frt|t jdjdg||gddd}ttfd d|DStt tfr>> from sympy import Parabola, Point, Ellipse, Line, Segment >>> p1 = Point(0,0) >>> l1 = Line(Point(1, -2), Point(-1,-2)) >>> parabola1 = Parabola(p1, l1) >>> parabola1.intersection(Ellipse(Point(0, 0), 2, 5)) [Point2D(-2, 0), Point2D(2, 0)] >>> parabola1.intersection(Line(Point(-7, 3), Point(12, 3))) [Point2D(-4, 3), Point2D(4, 3)] >>> parabola1.intersection(Segment((-12, -65), (14, -68))) [] zx yTr)cSsg|] }t|qSr)r.0irrr Fsz)Parabola.intersection..)setr#rcsg|]}|krt|qSrr r;orrr>QscSsg|] }t|qSrr@r;rrrr>Ssz5Entity must be two dimensional, not three dimensionalzWrong type of argument were putN)rr1 isinstancerlistrrr rsubs_argsr r r Zpointsrr TypeError)r rBr'r(Z parabola_eqresultrrAr intersection$sJ    *     zParabola.intersectioncCs|jj}|tjkr4|jjd}t|jjd|}nJ|dkr^|jjd}t|jjd|}n |j|j}t|jj |j }||j S)aP is a parameter of parabola. Returns ======= p : number or symbolic expression Notes ===== The absolute value of p is the focal length. The sign on p tells which way the parabola faces. Vertical parabolas that open up and horizontal that open right, give a positive value for p. Vertical parabolas that open down and horizontal that open left, give a negative value for p. See Also ======== https://www.sparknotes.com/math/precalc/conicsections/section2/ Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.p_parameter -4 rrr#) rr,rr-r0rrr%Z projectionr'r:)r r2r'pr(r8rrrr.Zs!   zParabola.p_parametercCsp|j}|jj}|tjkr6t|jd|j|jd}n6|dkr\t|jd|jd|j}n|j |d}|S)apThe vertex of the parabola. Returns ======= vertex : Point See Also ======== sympy.geometry.point.Point Examples ======== >>> from sympy import Parabola, Point, Line >>> p1 = Parabola(Point(0, 0), Line(Point(5, 8), Point(7, 8))) >>> p1.vertex Point2D(0, 4) rr#) rrr,rr-rr%r.r"rI)r rr2r/rrrr/s zParabola.vertex)NN)r'r()__name__ __module__ __qualname____doc__rpropertyr!r"rr&r1r:rrIr.r/rrrrrs(,     " , " 6 ,rN)rNZ sympy.corerZsympy.core.sortingrZsympy.core.symbolrrZsympy.geometry.entityrrZsympy.geometry.pointrr Zsympy.geometry.liner r r r rZsympy.geometry.ellipserZsympy.functionsrZsympy.simplifyrZsympy.solvers.solversrrrrrrs